Three identical capacitors C₁,C₂ and C₃ of capacitance \(6\mu F\) each are connected to a 12V battery as shown. Find charge on each capacitor

Find
(i) the charge on each capacitor
(ii) the equivalent capacitances of the network
(iii) the energy stored in the network of capacitors.

Which of the following figures cannot possibly represent electrostatic field lines?

Figures (a) and (b) show the field lines of a positive and negative point charge respectively

(a) Give the signs of the potential difference V_P – V_Q; V_B – V_A.
(b) Give the sign of the potential energy difference of a small negative charge between the points Q and P; A and B.
(c) Give the sign of the work done by the field in moving a small positive charge from Q to P.
(d) Give the sign of the work done by the external agency in moving a small negative charge from B to A.
(e) Does the kinetic energy of a small negative charge increase or decrease in going from B to A?

(a) Determine the electrostatic potential energy of a system consisting of two charges 7 μC and –2 μC (and with no external field) placed at (–9 cm, 0, 0) and (9 cm, 0, 0) respectively.
(b) How much work is required to separate the two charges infinitely away from each other?
(c) Suppose that the same system of charges is now placed in an external electric field E = A (1/r ²); A = 9 x 10⁵ NC^-1 m². What would the electrostatic energy of the configuration be?

(a) A comb run through one’s dry hair attracts small bits of paper. Why?
What happens if the hair is wet or if it is a rainy day? (Remember, a paper does not conduct electricity.)
(b) Ordinary rubber is an insulator. But special rubber tyres of aircraft are made slightly conducting. Why is this necessary?
(c) Vehicles carrying inflammable materials usually have metallic ropes touching the ground during motion. Why?
(d) A bird perches on a bare high power line, and nothing happens to the bird. A man standing on the ground touches the same line and gets a fatal shock. Why?